How to create a rotation animation with "Manipulate Centre Points" turned on?
You can do this by parenting the object to an empty and using rotation constraints.

First add an empty at the point you want the object to rotate around.  Then select the object and then the empty (in that order) and hit Ctrl+P to parent it to the empty.  Now you can animate the empty revolving around as desired.



Then select the object and go to the Constraints Properties panel and add a Limit Rotation constraint and enable the constraint on all three axes, leaving the Min and Max values at 0.